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- W2007108741 abstract "Abstract. The author with C. H. Kim and Y. Lee constructedinflnite families of elliptic curves over cubic number flelds K withprescribed torsion groups which occur inflnitely often. In this paper,we examine the Galois structures of such cubic number flelds K forthe families of elliptic curves with cyclic torsion. 1. IntroductionOver cubic number flelds K , it is proved in [4] that all the groupstructures occurring inflnitely often as torsion groups E ( K ) tors are ex-actly the following 38 types:(1.1)Z =N 1 Z ; N 1 = 1 i 16 ; 18 ; 20Z = 2Z ' Z = 2 N 2 Z ; N 2 = 1 i 7where K varies over all cubic number flelds and E varies over all ellipticcurves over K . In [3] the author with C. H. Kim and Y. Lee constructinflnite families of elliptic curves with torsion structures in Eq. (1.2) overcubic number flelds K .In this paper we examine the Galois structures of deflning flelds ofthe constructed inflnite families of elliptic curves with cyclic torsion in[3]. For our purpose, it is su–cient to consider the families of ellipticcurves with cyclic torsion groups which do not occur over Q. That is,we consider the following groups(1.2) Z" @default.
- W2007108741 created "2016-06-24" @default.
- W2007108741 creator A5008163300 @default.
- W2007108741 date "2014-05-15" @default.
- W2007108741 modified "2023-09-25" @default.
- W2007108741 title "GALOIS STRUCTURES OF DEFINING FIELDS OF FAMILIES OF ELLIPTIC CURVES WITH CYCLIC TORSION" @default.
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- W2007108741 doi "https://doi.org/10.14403/jcms.2014.27.2.205" @default.
- W2007108741 hasPublicationYear "2014" @default.
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